One of the earliest techniques of reachability analysis, the
hyperplane method, approximates reachable sets by
intersections of supporting halfspaces and by convex hulls of the
respective support points
[1]}, [2]}. More recent
techniques rely on a variety of additional classes of sets
including, e.g. ellipsoids, hyper-intervals, and zonotopes
[3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}.
As for reachable tubes, the standard approach today is to apply the
method proposed in [5]} or one of its extensions,
e.g. [6]}, [7]}, [4]}, [8]}, [9]}, which compute over-approximations in the form of
finite unions of zonotopes
[5]}, [6]}, [4]}
and of more general convex sets
[7]}, [8]}, [9]}.
As a result of such representation, disjointness from a polyhedral (or
convex) unsafe region can be verified by solving a linear (or convex)
feasibility problem. While the method is particularly efficient
and converges, i.e., it is capable of producing arbitrarily precise
over-approximations, its application is limited to the time-invariant
special case of REF . Its extension in
[10]} additionally allows for uncertain
coefficients \(A\)  and \(B\)  in REF , but does not converge
even if \(A\)  and \(B\)  are precisely known, in which case
REF  is again required to be time-invariant.
